Natalie Baddour

University of Ottawa | Université d'Ottawa, Mechanical Engineering, Faculty Member

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I hold a Bachelor of Science degree from Memorial University of Newfoundland, a Master of Mathematics degree from the University of Waterloo and a Ph.D. in Mechanical Engineering from the University of Toronto. I spent some time as a post-doc at both the University of Toronto and also at the University of Bath (U.K) as a Chevening Fellow. I also hold an A.R.C.T. diploma in piano performance from the Royal Conservatory of Toronto. I am now a full professor in the Department of Mechanical Engineering at the University of Ottawa.

I have worked in a variety of areas and applications. The common theme has always been the development of a model to represent a real-world problem and the analysis of what this model tells us about said real-world problem. These problems have tended to be dynamics/mechanics/vibrations type problems with a smattering of non-destructive testing or biomedical applications.

Current Research Interests:

Mathematical modeling, dynamics, vibrations, photoacoustics, mathematical methods (specifically Fourier methods at the moment).

Some information about projects I'm working on can be found at http://nbaddour.wordpress.com/projects/.
Phone: +1(613)562-5800 X2324
Address: Department of Mechanical Engineering
University of Ottawa
161 Louis Pasteur
Ottawa, Ontario
K1N 6N5
Canada

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Books by Natalie Baddour

Ultrasonic Tethering to Enable Side-by-Side Following for Powered Wheelchairs

Sensors, 2018

In social situations, people who use a powered wheelchair must divide their attention between nav... more In social situations, people who use a powered wheelchair must divide their attention between navigating the chair and conversing with people. These conversations could lead to increased mental stress when navigating and distraction from maneuvering the chair. As a solution that maintains a good conversation distance between the wheelchair and the accompanying person (Social Following), a wheelchair control system was developed to provide automated side-by-side following by wirelessly connecting the wheelchair to the person. Two ultrasonic range sensors and three piezoelectric ultrasonic transducers were used to identify the accompanying person and determine their position and heading. Identification involved an ultrasonic beacon worn on the person's side, at hip level, and receivers on the wheelchair. A drive control algorithm maintained a constant conversation distance along the person's trajectory. A plug-and-play prototype was developed and connected to a Permobil F5 Corpus wheelchair with a modified Eightfold Technologies SmartChair Remote. Results demonstrated that the system can navigate a wheelchair based on the accompanying person's trajectory, which is advantageous for users who require hands-free wheelchair control during social activities.

format_quoteAn automated side-by-side following system was designed to alleviate mental stress, enabling wheelchair users to converse while safely navigating.format_quote

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Recent Advances in Vibrations Analysis

This book covers recent advances in modern vibrations analysis, from analytical methods to applic... more This book covers recent advances in modern vibrations analysis, from analytical methods to applications of vibrations analysis to condition monitoring. Covered topics include stochastic finite element approaches, wave theories for distributed parameter systems, second other shear deformation theory and applications of phase space to the identifications of nonlinearities and transients. Chapters on novel condition monitoring approaches for reducers, transformers and low earth orbit satellites are included. Additionally, the book includes chapters on modelling and analysis of various complex mechanical systems such as eccentric building systems and the structural modelling of large container ships.

A Modelling and Vibration Analysis of Spinning Disks

This thesis considers a modelling and vibration analysis of thin spinning disks. Both in-plane a... more This thesis considers a modelling and vibration analysis of thin spinning disks. Both in-plane and transverse vibrations are considered. Kirchhoff and von Karman theory of plates along with Hamilton's principle are used to derive linear and nonlinear equations of motion for the vibrations of a spinning plate. In-plane and rotary inertias are naturally accounted for in this procedure. The resulting equations are similar to those previously derived in the literature but contain some additional terms. These linear and nonlinear equations are subsequently analyzed. New orthogonality properties of the in-plane modes are derived and are used to construct solutions to the linear, forced in-plane vibration problem. The linear transverse vibration equations are derived with new terms. These new terms are explained physically and their effect on the frequencies of vibrations is analyzed. Nonlinearly coupled transverse and in-plane vibrations are considered while including the effect of in-plane inertia which has always been neglected by other researchers. It is found that the inclusion of in-plane inertia introduces the possibility of internal resonance between the in-plane and transverse modes of vibration.

$eh=a,+a2 isaconstant. [f equation (5.107) is substituted into equation (5.106) solution S(c,T, De, Dr, t) of the Hamilton-Jacobi equation associated with H\)(c. r. p.. pr).$

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Papers by Natalie Baddour

Design and evaluation of a passive inertial mass device for car suspension system

by Natalie Baddour and Shuai Yang

International Journal of Vehicle Design, 2019

A new adaptive nylon flywheel is proposed, which can achieve passive vibration control by generat... more A new adaptive nylon flywheel is proposed, which can achieve passive vibration control by generating variable equivalent mass. With changing rotational speed, the location of sliders in the slots changes, which leads to the creation of variable equivalent mass. Due to the light weight and high strength of the nylon material, a higher changing ratio of equivalent mass can be achieved. To verify the performance of the adaptive nylon flywheel, the inverse screw system was applied. By using zero, impulse and sinusoidal input as road excitation, the proposed car suspension system was evaluated from riding comfort and tyre grip. Simulation results show the proposed suspension system provides better performance than traditional suspension systems under most circumstances.

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Discrete Two-Dimensional Fourier Transform in Polar Coordinates Part I: Theory and Operational Rules

Mathematics, 2019

The theory of the continuous two-dimensional (2D) Fourier transform in polar coordinates has been... more The theory of the continuous two-dimensional (2D) Fourier transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

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Maintaining stable transtibial amputee gait on level and simulated uneven conditions in a virtual environment

Disability and Rehabilitation: Assistive Technology, 2019

Purpose: This research compares gait strategies to maintain stable gait over a variety of non-lev... more Purpose: This research compares gait strategies to maintain stable gait over a variety of non-level walking conditions for individuals with a transtibial amputation and able-bodied individuals. Methods: Twelve people with unilateral transtibial amputation and twelve able-bodied individuals walked on a self-paced treadmill in a park-like virtual environment with level and continuous perturbation conditions. Walking stability was quantified by margin-of-stability, step parameters (walking speed, temporal and spatial parameters, and foot clearance), and gait variability (standard deviations for margin-of-stability, step parameters, and root-mean-square of trunk acceleration). Results and conclusions: For non-level conditions, able-bodied and transtibial groups had greater rootmean-square of trunk acceleration and walked with a cautious and variable step strategy by changing speed, step width, foot clearance, margin-of-stability, and increasing step variability. Overall, able-bodied and transtibial amputee participants adopted similar strategies to maintain stable gait over non-level conditions, but the amputee group was more variable than the able-bodied group. These results demonstrated the importance of measuring gait variability, including trunk acceleration and step variability measures, when quantitatively assessing mobility for individuals with a transtibial amputation. ä IMPLICATIONS FOR REHABILITATION Able-bodied and transtibial amputee groups adapted gait biomechanics for simulated uneven conditions. Adaptations for non-level conditions included increasing step width, margin-of stability, minimum foot clearance, and varying speed. Gait was also more variable for non-level conditions, with greater variability for transtibial amputee participants compared to able-bodied participants. These results highlight the importance of measuring variability when performing comprehensive walking assessment, particularly for active individuals who achieve maximal performance on standard assessments yet report functional limitations in daily living.

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Shear wave propagation in viscoelastic media: validation of an approximate forward model

Physics in Medicine & Biology, 2019

Many approaches to elastography incorporate shear waves; in some systems these are produced by ac... more Many approaches to elastography incorporate shear waves; in some systems these are produced by acoustic radiation force (ARF) push pulses. Understanding the shape and decay of propagating shear waves in lossy tissues is key to obtaining accurate estimates of tissue properties, and so analytical models have been proposed. In this paper, we reconsider a previous analytical model with the goal of obtaining a computationally straightforward and efficient equation for the propagation of shear waves from a focal push pulse. Next, this model is compared with an experimental optical coherence tomography (OCT) system and with finite element models, in two viscoelastic materials that mimic tissue. We find that the three different cases-analytical model, finite element model, and experimental results-demonstrate reasonable agreement within the subtle differences present in their respective conditions. These results support the use of an efficient form of the Hankel transform for both lossless (elastic) and lossy (viscoelastic) media, and for both short (impulsive) and longer (extended) push pulses that can model a range of experimental conditions.

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Failure and life evaluation of EB-PVD thermal barrier coatings using temperature-process-dependent model parameters

Corrosion Science, 2019

Using experimentally measured temperature-process-dependent model parameters, the failure analysi... more Using experimentally measured temperature-process-dependent model parameters, the failure analysis and life evaluation were conducted for electron beam-physical vapor deposition thermal barrier coatings (EB-PVD TBCs) with Pt-modified β-NiAl bond coats deposited on Ni-base single crystal superalloys. The failure analysis and life model were applied to two failure modes of A and B identified experimentally subjected to thermal cyclic process. The rumpling effect and the associated roughness of the constituent coating layers were shown to play a key role in evaluating the coating's failure and life. The experimentally determined temperature-dependent thickness of thermally grown oxide (TGO), interfacial roughness, elastic moduli of the constituent coatings and their coefficients of thermal expansion were incorporated into the life prediction model. The maximum average rumpling amplitude of the bond coat/TGO interface associated with bond coat rumpling was used in failure analysis and life evaluation for the failure mode A. The global wavelength related to the interface rumpling and its radius curvature were identified as essential parameters in life evaluation, and the predicted life results for failure mode A were verified by existing furnace cyclic test data. For the failure mode B, the crack growth rate along the TGO/top coat interface was calculated using the crack length dependent fracture toughness.

$Fig. 4. A crack length dependence fracture toughness [1]. Fig. 3. The measured and fitted maximum crack length versus high tempera ture exposure time. Each cycle consists of 2h at maximum temperature anc 15 min forced air-cooling to room temperature [50].$

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A shape-independent approach to modelling gear tooth spalls for time varying mesh stiffness evaluation of a spur gear pair

Mechanical Systems and Signal Processing, 2019

Accurately evaluating the gear mesh stiffness with tooth fault(s) plays an important role in gear... more Accurately evaluating the gear mesh stiffness with tooth fault(s) plays an important role in gear dynamic simulations. Common approaches to evaluating the gear TVMS with spall assume a specific geometry (rectangular, round, elliptical, V-shape etc.) to approximate the features of the spall. The accuracy of geometry-based methods on modeling gear tooth spall depends on how close the utilized geometry is to the actual shape of the spall. In practice , gear tooth spalls often occur in very irregular shapes and may also have randomly distributed features under multi-spall conditions. Due to shape irregularities and uncertainties in their distribution, it is often difficult to apply existing methods to accurately evaluate gear TVMS with spalls as observed in practice. To address these shortcomings, this paper proposes a shape-independent method to model tooth spall(s) based on defect ratios instead of a specific geometry. The proposed method is applicable to tooth spalls of various sizes, shapes, numbers and distribution conditions, and thus is capable of modeling any kind of tooth spall. A powerful advantage of the proposed method is that to change the type of spall being modelled, only the functions of the defect ratios need to be modified rather than the entire algorithm. Therefore, the proposed method is general in nature and much easier to implement in practice. The effectiveness of the proposed shape-independent approach to modelling different kinds of tooth spalls is validated by finite element results.

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Waveform engineering analysis of photoacoustic radar chirp parameters for spatial resolution and SNR optimization

Photoacoustics, 2019

Recent developments in photoacoustics have witnessed the implementation of a radar matched-filter... more Recent developments in photoacoustics have witnessed the implementation of a radar matched-filtering methodology into the continuous wave photoacoustic modality. The main merit of using matched filtering in continuous photoacoustics is the improvement in signal to noise ratio (SNR), but the correlation process may result in a loss of resolution. It is possible to enhance both SNR and resolution by matched-filtering and pulse compression with a frequency chirp. However, the theory behind the effect of the chirp parameters on both SNR and resolution is still not clear. In this paper, the one-dimensional theory of the photoacoustic radar with a pulse compressed linear frequency modulated sinusoidal laser chirp is developed. The effect of the chirp parameters on the corresponding photoacoustic signal is investigated, and guidelines for choosing the chirp parameters for resolution and SNR optimization are given based on theory and simulations. The results show that by judiciously manipulating the center frequency, bandwidth, and duration, the resolution and SNR can be easily enhanced.

format_quoteAdvantages of chirp modulated PAR include higher frame rates, portability, and improved diagnostic power through dual imaging.format_quote

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Design, development, and evaluation of a local sensor-based gait phase recognition system using a logistic model decision tree for orthosis-control

Journal of neuroengineering and rehabilitation, 2019

Background: Functionality and versatility of microprocessor-controlled stance-control knee-ankle-... more Background: Functionality and versatility of microprocessor-controlled stance-control knee-ankle-foot orthoses (M-SCKAFO) are dictated by their embedded control systems. Proper gait phase recognition (GPR) is required to enable these devices to provide sufficient knee-control at the appropriate time, thereby reducing the incidence of knee-collapse and fall events. Ideally, the M-SCKAFO sensor system would be local to the thigh and knee, to facilitate innovative orthosis designs that allow more flexibility for ankle joint selection and other orthosis components. We hypothesized that machine learning with local sensor signals from the thigh and knee could effectively distinguish gait phases across different walking conditions (i.e., surface levels, walking speeds) and that performance would improve with gait phase transition criteria (i.e., current states depend on previous states). Methods: A logistic model decision tree (LMT) classifier was trained and tested (five-fold cross-validation) on gait data that included knee flexion angle, thigh-segment angular velocity, and thigh-segment acceleration. Twenty features were extracted from 0.1 s sliding windows for 30 able-bodied participants that walked on different surfaces (level, down-slope, up-slope, right cross-slope, left cross-slope) at a various walking speeds (self-paced (1.33 m/s, SD = 0.04 m/s), 0.8, 0.6, 0.4 m/s). The LMT-based GPR model was also tested with another validation set containing similar features and surfaces from 12 able-bodied volunteers at self-paced walking speeds (1.41 m/s, SD = 0.34 m/s). A "Transition Sequence Verification and Correction" (TSVC) algorithm was applied to correct for continuous class prediction and to improve GPR performance. Results: The LMT had a tree size of 1643 with 822 leaf nodes, with a logistic regression model at each leaf node. The local sensor LMT-based GPR model identified loading response, push-off, swing, and terminal swing phases with overall classification accuracy of 98.38 for the initial training set (five-fold cross-validation) and 90. 60% for the validation set. Applying TSVC increased classification accuracy to 98.72% for the initial training set and 98.61% for the validation set. Sensitivity, specificity, precision, F-score, and Matthew's correlation coefficient results suggest strong evidence for the feasibility of an LMT-based GPR system for real-time orthosis control. Conclusions: The novel machine learning GPR model that used sensor features local to the thigh and knee was viable for dynamic knee-ankle-foot orthosis-control. This highly accurate GPR model was generalizable when combined with TSVC. Our approach could reduce sensor system complexity as compared with other M-SCKAFO approaches, thereby enabling customizable advantages for end-users through modular unit orthosis designs.

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Multiple time-frequency curve extraction Matlab code and its application to automatic bearing fault diagnosis under time-varying speed conditions

MethodsX, 2019

Vibration signal analysis is an important technique for bearing fault diagnosis. For bearings ope... more Vibration signal analysis is an important technique for bearing fault diagnosis. For bearings operating under constant rotational speed, faults can be diagnosed in the frequency domain since each type of fault has a specific Fault Characteristic Frequency (FCF), which is proportional to the shaft rotational speed. However, bearings often operate under time-varying speed conditions. Additionally, the measurement of the time-varying rotational speed requires instruments, such as tachometers, which leads to extra cost and installation. With the development of time-frequency analysis, the time-varying FCFs manifest as curves in the Time-Frequency Representation (TFR). It has been shown that extracting multiple time-frequency curves from the TFR and then identifying the Instantaneous Fault Characteristic Frequency (IFCF) and Instantaneous Shaft Rotational Frequency (ISRF), bearing faults can be automatically diagnosed under time-varying speed conditions without using tachometers. However, the existing method used to identify the IFCF and the ISRF may lead to inaccurate results. In this study, the complete MATLAB © codes and a more reliable approach to use Multiple Time-Frequency Curve Extraction (MTFCE) for automatic bearing fault diagnosis under time-varying speed conditions are presented. A Multiple time-frequency curve extraction (MTFCE) Matlab code is presented to extract multiple curves from the TFR. Custom Matlab code for automatic bearing fault diagnosis under time-varying speed conditions without using tachometer data via the MTFCE is given and explained. A new parameter, the allowable variance of the curve-to-curve ratio, is proposed to identify the IFCF and ISRF more reliably.

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Discrete Two-Dimensional Fourier Transform in Polar Coordinates Part I: Theory and Operational Rules

Mathematics, 2019

format_quoteCurrent literature lacks a discrete 2D Fourier transform in polar coordinates despite prior considerations for computational methods.format_quote

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Disability and Rehabilitation: Assistive Technology Maintaining stable transtibial amputee gait on level and simulated uneven conditions in a virtual environment

Disability and Rehabilitation: Assistive Technology , 2019

Purpose: This research compares gait strategies to maintain stable gait over a variety of non-lev... more Purpose: This research compares gait strategies to maintain stable gait over a variety of non-level walking conditions for individuals with a transtibial amputation and able-bodied individuals.

Methods: Twelve people with unilateral transtibial amputation and twelve able-bodied individuals walked on a self-paced treadmill in a park-like virtual environment with level and continuous perturbation conditions. Walking stability was quantified by margin-of-stability, step parameters (walking speed, temporal and spatial parameters, and foot clearance), and gait variability (standard deviations for margin-of-stability, step parameters, and root-mean-square of trunk acceleration).

Results and conclusions: For non-level conditions, able-bodied and transtibial groups had greater root-mean-square of trunk acceleration and walked with a cautious and variable step strategy by changing speed, step width, foot clearance, margin-of-stability, and increasing step variability. Overall, able-bodied and transtibial amputee participants adopted similar strategies to maintain stable gait over non-level conditions, but the amputee group was more variable than the able-bodied group. These results demonstrated the importance of measuring gait variability, including trunk acceleration and step variability measures, when quantitatively assessing mobility for individuals with a transtibial amputation.

Implications for rehabilitation
Able-bodied and transtibial amputee groups adapted gait biomechanics for simulated uneven conditions.

Adaptations for non-level conditions included increasing step width, margin-of stability, minimum foot clearance, and varying speed.

Gait was also more variable for non-level conditions, with greater variability for transtibial amputee participants compared to able-bodied participants.

These results highlight the importance of measuring variability when performing comprehensive walking assessment, particularly for active individuals who achieve maximal performance on standard assessments yet report functional limitations in daily living.

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Modelling Thermal Conductivity of Porous Thermal Barrier Coatings

Thermal conductivity of porous thermal barrier coatings was evaluated using a newly developed fiv... more Thermal conductivity of porous thermal barrier coatings was evaluated using a newly developed five-phase model. It was demonstrated that porosities distributed in coating strongly affect thermal conductivity. The decisive reason for this change in thermal conductivity can be traced back to defect morphology and its orientation, depending on the coating deposition technique and process parameters used during deposition. In this paper, the Bruggeman's two-phase model was used as a reference, and a five-phase model was developed to evaluate the thermal conductivity of porous coatings. This approach uses microstructural details of the shape, size, orientation and volumetric fraction of defects of coatings as input parameters. The proposed model can predict thermal conductivity values better than the previous two-phase model.

$Figure 4. Shape factor F as a function of the axial ratio a/c of the spheroid (Reprinted with permission from [41]. Copyright 2018 Elsevier). and c (c > a), the spheroid is stretched horizontally to obtain the shape of an oblate spheroid. The shape factor F for oblate (lamellas) lies between 0 and 1/3. There is an exception when the lamellae are oriented normal to the heat flux, in which case X is equal to 1. A prolate shape spheroid is obtained when pores are stretched in the vertical direction and there is a very little area in the horizontal direction. The shape factor F for prolate pores lies between 1/3 to 1/2. The value of X can also be modelled using a cylindrical shape as well. For a cylinder, the X value depends on the orientation of the major axis a. The values depend on whether the ‘a’ axis is parallel (X = 1), randomly oriented (X = 1.66) and/or perpendicular (X = 2). Figure 5 shows the ratio k/km as a function of the volumetric fraction of porosity at different orientations with respect to the heat flux given by the Bruggeman model in Equation (6).$

$Figure 5. The ratio k/km vs. the volumetric fraction of porosity as estimated by Equation (6) for lamellae (F = 0.0369) with the revolution axis (A) parallel, (B) perpendicular and (C) randomly oriented at 60° [50].$

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Theory and operational rules for the discrete Hankel transform

Journal of the Optical Society of America, 2015

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate ... more Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

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Feature Selection for Wearable Smartphone- Based Human Activity Recognition with Able bodied, Elderly, and Stroke Patients

by Edward Lemaire and Natalie Baddour

Human activity recognition (HAR), using wearable sensors, is a growing area with the potential to... more Human activity recognition (HAR), using wearable sensors, is a growing area with the potential to provide valuable information on patient mobility to rehabilitation specialists. Smart-phones with accelerometer and gyroscope sensors are a convenient, minimally invasive, and low cost approach for mobility monitoring. HAR systems typically pre-process raw signals , segment the signals, and then extract features to be used in a classifier. Feature selection is a crucial step in the process to reduce potentially large data dimensionality and provide viable parameters to enable activity classification. Most HAR systems are custom-ized to an individual research group, including a unique data set, classes, algorithms, and signal features. These data sets are obtained predominantly from able-bodied participants. In this paper, smartphone accelerometer and gyroscope sensor data were collected from populations that can benefit from human activity recognition: able-bodied, elderly, and stroke patients. Data from a consecutive sequence of 41 mobility tasks (18 different tasks) were collected for a total of 44 participants. Seventy-six signal features were calculated and subsets of these features were selected using three filter-based, classifier-independent, feature selection methods (Relief-F, Correlation-based Feature Selection, Fast Correlation Based Filter). The feature subsets were then evaluated using three generic classifiers (Naïve Bayes, Support Vector Machine, j48 Decision Tree). Common features were identified for all three populations, although the stroke population subset had some differences from both able-bodied and elderly sets. Evaluation with the three classifiers showed that the feature subsets produced similar or better accuracies than classification with the entire feature set. Therefore, since these feature subsets are classifier-independent, they should be useful for developing and improving HAR systems across and within populations.

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A direct method for solving inverse eigenvector problems for Jacobi and Tridiagonal Matrices

This paper investigates the use of a direct method for solving inverse eigenvector problems invol... more This paper investigates the use of a direct method for solving inverse eigenvector problems involving Jacobi or tridiagonal matrices. Specifically, this paper demonstrates the application of the method to oscillating mass-spring systems having fixed-free boundary conditions. The method demonstrates how to reconstruct Jacobi, mass and stiffness matrices from knowledge of one or two eigenvectors and various physical parameters. Three algorithms are proposed and examples are given. The solvability of the method is discussed and its advantages over other numerical methods are considered.

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Evaluation of a Variable Resistance Orthotic Knee Joint

Knee-ankle-foot orthoses (KAFOs) are full leg braces for individuals with knee extensor weakness,... more Knee-ankle-foot orthoses (KAFOs) are full leg braces for individuals with knee extensor weakness, designed to support the person during weight bearing activities by preventing knee flexion. KAFOs typically result in an unnatural gait pattern and are primarily used for level ground walking. A novel variable resistance orthotic knee joint, the Ottawalk-Variable Speed (OWVS), was designed to address these limitations. This paper presents a pilot test to evaluate the OWVS functional performance during walking and stair descent. A carbon-fiber KAFO was adjusted for an able-bodied participant by a certified orthotist, with a standard orthotic single axis knee joint on the medial side and the OWVS on the lateral side. The participant performed level ground walking (stance-control, open, closed) and stair descent tests. The operator was able to manually switch between closed mode in terminal swing to open mode in terminal stance for stancecontrol walking. Knee angle kinematics were similar between open and stance control modes. For stair descent, resistance settings supported the participant as they lowered their body to the next step, but with smaller range of motion compared to the open setting. The Ottawalk-Variable Speed design successfully controls knee flexion during stance and stair descent, with one lateral control joint. Mode switching was fast and appropriate. This microprocessor controlled SCKAFO has a low profile that fits beneath clothing and the variable resistance design will allow people to negotiate different terrain types.

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On Using Alternative Admissible Functions to Find the Natural Frequencies of a Beam with Attachments

In vibrations analysis, expansions with system eigenfunctions lead to low order matrices but ofte... more In vibrations analysis, expansions with system eigenfunctions lead to low order matrices but often result in numerical instabilities. In this paper, the problem of using alternative functions to find the natural frequencies of a beam with attachments is considered. A set of admissible functions consisting of polynomials up to 2 nd degree followed by a cosine Fourier series is utilized as an alternative to the traditional eigenfunctions to derive mass and stiffness matrices of an unconstrained Euler-Bernoulli beam. Boundary conditions are implemented via a penalty method approach. These matrices are then modified to account for the presence of added lumped elements. To verify the validity of this approach, the results are tabulated for a case of a torsional spring added to a simply supported beam and a case of a combination of a linear spring with a lumped mass grounded at a certain point along the beam. The results are compared against those of Finite Element Analysis and those obtained by an assumed modes approach, and the discrepancies are established. Close agreement was observed in both scenarios, attesting to the accuracy and effictiveness of the novel approach.

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